{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D4OOJKAOGUPRZDISPUNH3YTPFF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"08a6f4c7bcee963ad7fdbb82f10bebff791b21c2c9852ef7ff82ff5296987ad8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-14T17:57:39Z","title_canon_sha256":"c793628393c44c7b5331752bd78070f70f4d4ac61691a57602d5b1532684035e"},"schema_version":"1.0","source":{"id":"1702.04313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04313","created_at":"2026-07-05T00:56:22Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04313v2","created_at":"2026-07-05T00:56:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04313","created_at":"2026-07-05T00:56:22Z"},{"alias_kind":"pith_short_12","alias_value":"D4OOJKAOGUPR","created_at":"2026-07-05T00:56:22Z"},{"alias_kind":"pith_short_16","alias_value":"D4OOJKAOGUPRZDIS","created_at":"2026-07-05T00:56:22Z"},{"alias_kind":"pith_short_8","alias_value":"D4OOJKAO","created_at":"2026-07-05T00:56:22Z"}],"graph_snapshots":[{"event_id":"sha256:3919896fba031646def96c26cc11b92f482d128dc4a7e7b8890ad60662aee741","target":"graph","created_at":"2026-07-05T00:56:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1702.04313/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the terminal-pairibility problem in the case when the base graph is a complete bipartite graph, and the demand graph is also bipartite with the same color classes. We improve the lower bound on maximum value of $\\Delta(D)$ which still guarantees that the demand graph $D$ is terminal-pairable in this setting. We also prove a sharp theorem on the maximum number of edges such a demand graph can have.","authors_text":"Ervin Gy\\H{o}ri, Lucas Colucci, P\\'eter L. Erd\\H{o}s, Tam\\'as R\\'obert Mezei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-14T17:57:39Z","title":"Terminal-Pairability in Complete Bipartite Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04313","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:19049f0084986faa2c0634b77c817972db213429c1664c7bdc5622b8f0cdd36c","target":"record","created_at":"2026-07-05T00:56:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"08a6f4c7bcee963ad7fdbb82f10bebff791b21c2c9852ef7ff82ff5296987ad8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-14T17:57:39Z","title_canon_sha256":"c793628393c44c7b5331752bd78070f70f4d4ac61691a57602d5b1532684035e"},"schema_version":"1.0","source":{"id":"1702.04313","kind":"arxiv","version":2}},"canonical_sha256":"1f1ce4a80e351f1c8d127d1a7de26f2973395dd402baff5b4eb4529b7b45a59a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f1ce4a80e351f1c8d127d1a7de26f2973395dd402baff5b4eb4529b7b45a59a","first_computed_at":"2026-07-05T00:56:22.052910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:56:22.052910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sN/uq4KUAW1TfaPiTZqQpXzh5thXkVx5VLsBoeRMfJzItPIxrCLO/H7CuiKHS8w+na6Lhl3P689AY1hy0ftRBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:56:22.053361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19049f0084986faa2c0634b77c817972db213429c1664c7bdc5622b8f0cdd36c","sha256:3919896fba031646def96c26cc11b92f482d128dc4a7e7b8890ad60662aee741"],"state_sha256":"c9fb215e940018e13ba7d9b3af5d0e84d7d3a252b2b44e07f751a218a3067c8a"}